The simple interest on a sum for 5 years at 8% p.a. is ₹3,960. What will be the simple interest on the same sum for `6 (2)/(3)` years at 12%p.a ?

Options

A. ₹6,600
B. ₹5,280
C. ₹7,920
D. ₹8,000

Answer

To solve the problem step by step, we will first find the principal amount using the information given about the simple interest for the first scenario, and then use that principal to calculate the simple interest for the second scenario.

### Step 1: Find the Principal Amount

We know the formula for simple interest (SI):
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

From the question, we have:
- \( SI = 3960 \)
- \( R = 8\% \)
- \( T = 5 \) years

Substituting the values into the formula:
\[ 3960 = \frac{P \times 8 \times 5}{100} \]

### Step 2: Simplify the Equation

Now, we simplify the equation:
\[ 3960 = \frac{40P}{100} \]
\[ 3960 = \frac{P}{2.5} \]

### Step 3: Solve for Principal \( P \)

To find \( P \), we multiply both sides by 2.5:
\[ P = 3960 \times 2.5 \]
Calculating this gives:
\[ P = 9900 \]

### Step 4: Calculate Simple Interest for the New Scenario

Now, we need to find the simple interest for \( 6 \frac{2}{3} \) years at \( 12\% \) per annum. First, convert \( 6 \frac{2}{3} \) years into an improper fraction:
\[ 6 \frac{2}{3} = \frac{20}{3} \text{ years} \]

Now, using the simple interest formula again:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 9900 \)
- \( R = 12\% \)
- \( T = \frac{20}{3} \)

Substituting these values into the formula:
\[ SI = \frac{9900 \times 12 \times \frac{20}{3}}{100} \]

### Step 5: Simplify the Calculation

Calculating the above expression:
\[ SI = \frac{9900 \times 12 \times 20}{300} \]
\[ SI = \frac{9900 \times 240}{300} \]
\[ SI = \frac{2376000}{300} \]
\[ SI = 7920 \]

### Final Answer

Thus, the simple interest on the same sum for \( 6 \frac{2}{3} \) years at \( 12\% \) per annum is **₹7920**.

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